bcorey,
I have also taught self defense to several women who had previously been a victim of some type of violence. If this is your first time dealing with this type of student, stand by for one of the most challenging, and yet rewarding, teaching experiences of your life!
One woman in particular comes to mind:
She was much like the woman you describe; she even had difficulty looking me in the eye while I was just casually talking to her before and after class. Like yourself, I was focusing on the Training Mission materials. She was very fearful of any kind of contact and was also reluctant to use the eye attacks on the BOB. To make a long story short, three months later she certified Level One in the Unarmed Combatives material and even attended one of the seminars when Hock came to Meridian. She continued to train with me for about 6 more months and continued to improve in every aspect of the material that we covered. She started looking me in the eye, standing up straight and attacking the BOB (and even myself!

) with aggression and confidence.
Fast forward a year:
Lo and behold, who is standing guard at the front gate as I drive into work? It's her! We both get a good laugh and do some catching up and she thanks me for helping her get her confidence and her life back. I also came to find out that she has become quite the little tigress whenever the security force does their training.
So, I agree with the majority of the advice given already:
1) Take your time. Patience and praise will definitely be key elements for a successful outcome.
2) If applicable, use the "Mama Bear" tactic already mentioned by Canuk; that's been a real winner for me.
3) Be especially mindful of her (and your own!) body language as you speak and even approach her to demonstrate a technique. Learning to recognize when the "fear factor" is mounting will enable you to change tactics quickly and regroup without ending a session prematurely.
In my class I was able to demonstrate on one of my training partners and let the ladies train with a partner they felt comfortable with until their confidence level improved. You might not have that luxury if she's a personal client.
"Excuse me if I sound crude, but is this lady damaged goods from being previously attacked? Or is this a case of a person that just doesn't have the grit to get nasty in order to preserve their own life?"
You don't sound crude to me; you sound concerned. That's a great start! Regardless of how she came to be this way, you have the opportunity to give her the tools she could use to possibly overcome her circumstances. I wish you, and her, the best of luck!
Please keep us posted! (Good luck!)